1. Field of the Invention
The present invention relates to a method for the estimation of seismic velocities and more particularly to a method for the tomographic estimation of seismic transmission velocities.
2. Related Prior Art
Depth migration can estimate the locations of seismic reflectors in the earth from surface reflection seismic data. Migration requires a model of how seismic velocities change in the earth. However, these quantities cannot be measured directly. If the velocity model is incorrect, then migration will locate reflectors incorrectly.
Depth migration can also create images of seismic reflectors in the earth from single constant-offset seismic gathers, that is, from pairs of sources and receivers with equal horizontal separation. Since different offsets measure different angles of reflection, we can expect some differences in the amplitudes and phase of migrated reflectors from different offsets. The positions of migrated reflectors should, however, be consistent over offset if the model truly represents the local seismic velocities of recorded waves.
Much of the prior art demonstrates the feasibility of traveltime tomography, and the difficulty of optimizing velocities directly from migrated images. Traveltime tomography assumes that traveltimes have been measured along previously estimated raypaths with known endpoints. Well known algorithms then adjust the velocities along these overlapping raypaths to reduce errors in the modeled traveltimes. Because raypaths have locally minimum traveltimes, these adjustments to velocities can correct traveltime errors to first order without adjusting the positions of raypaths. The improved velocity model leads to an improved estimate of the raypaths, and vice-versa.
Reflected raypaths require the iterative estimation of an additional unknown, the positions at which raypaths reflect. Once these reflection points are known, then conventional means of traveltime tomography can estimate the velocities and intervening raypaths. Similarly, improved velocities allow improved estimates of the positions of reflectors.
Previous methods of estimating velocities from migrated data have not attempted to use traveltime tomography directly on migrated data. Some approaches have used migrations to locate reflectors and have then used the original unmigrated data to pick traveltimes. Others have attempted to measure the effect of perturbed velocities directly on the positions of migrated reflectors, thus losing the simple, well understood traveltime techniques available.
Examples of methods by which prior art has illustrated ways of estimating transmission velocities are as follows.
In the publication Numerical Recipes, Press et al, 1986, Cambridge Univ. Press, Chapter 16, "Two Point Boundary Value Problems", discusses numerical shooting and relaxation methods.
The publication by Society of Exploration Geophysicists expanded abstracts from the 1989 International Meeting and Exposition included an article titled "Efficient Seismic Tracing Using Graph Theory" by T. J. Moser. This article discussed a method which proposed that the shortest path method is an efficient, accurate and flexible way to compute raypaths. Not only rays corresponding to first arrivals can be found, but also reflections on interfaces and other later arrivals. The method can be generalized and then applied to a much wider class of problems, like modeling of non-point sources, exploding reflectors and migration of traveltime data. Other graphtheoretical algorithms, like the second shortest path procedure and the re-optimization of shortest paths, have practical applications in seismic technology.
Society of Exploration Geophysicists expanded abstracts from the 1989 International Meeting and Exposition, also included an article by John E. Vidale titled "Finite-Difference Calculation of Traveltimes in 3-D". This article stated that the travel times of first arriving seismic rays through most velocity structures can be rapidly, computed on a three-dimensional numerical grid by finite-difference extrapolation. Head waves are properly treated and shadow zones are filled by the appropriate diffractions. Differences of less than 0.11 percent were found between the results of this technique and ray-tracing for a complex model. This scheme has proven useful for earthquake location, and shows promise as an inexpensive, well-behaved substitute for ray-tracing in forward-modeling and Kirchhoff inversion applications.
U.S. Pat. No. 4,330,872, "Common-Offset-Distance Seismic Trace Filtering", issued to Robert H. Bratton relates to a multiple coverage seismic exploration technique providing for a plurality of seismic trace recordings along a line of exploration. From these recordings, sets of common-offset-distance traces are gathered. Initial estimates are made of the apparent dips associated with the seismic reflection signals across each set of common-offset-distance traces. These initial dip estimates are smoothed and the sets of common-offset-distance traces filtered along the apparent dips associated with the smoothed dip estimates to enhance the signal-to-noise ratio of the primary reflection signals.
U.S. Pat. No. 4,839,869, "Methods for Processing Converted Wave Seismic Data", issued to Chris T. Corcoran relates to methods for processing converted wave seismic data which includes, fractional point gathering of the data in a manner consistent with a selected velocity model, dynamic correction of the data using parameters measured from the data to account for the asymmetric travel path of the converted wave rays and stacking the dynamically corrected data. Methods are also provided for updating the velocity model.